Find the complete factored form of the polynomial 28 a^6 b^6 + 4 a^4 b^2

The complete factored form is 4 a^4 b² (7 a² b^4 + 1)

Step-by-step explanation:

* Lets explain how to solve the problem

- To factorize a binomial;

# Find the greatest common factors of the coefficient and the variable

# Check the binomial if it is different of two squares or sum of two

cubes or different of two cubes

* Lets solve the problem

∵ 28 a^6 b^6 + 4 a^4 b²

- Lets find the greatest common factors of the coefficients

∵ The greatest factor of 28 and 4 is 4

∴ 28 a^6 b^6 + 4 a^4 b² = 4 (7 a^6 b^6 + a^4 b²)

- Lets find the greatest common factors of the variables

∵ The greatest common factors of a^6 and a^4 is a^4

∵ The greatest common factors of b^6 and b² is b²

∴ 4 (7 a^6 b^6 + a^4 b²) = 4 a^4 b² (7 a² b^4 + 1)

- Lets check the bracket

∵ There is no common factor in the bracket (7 a² b^4 + 1)

∴ The complete factored form of 28 a^6 b^6 + 4 a^4 b^2 is

4 a^4 b² (7 a² b^4 + 1)